1. Complete partials with respect to ?” and ?# for the following: ? = &?”.?#

U=2 X1 + X2 + 10X1X2

U=(?#” + ?#)# + (?”?#)+

2. Prove the equal marginal principle/rule for optimization using two goods. Illustrate with a diagram to bring together your analysis.

Remember that one of the crucial steps to proving this is the following intuition: 0 = MUX1.∆ X1+ MUX2.∆ X2

3. Prove that indifference curves cannot intersect.

4. Julio receives utility from consuming food (F) and clothing (C) as given by the utility function U(F,C)=FC. In addition, the price of food is $2 per unit, the price of clothing is $10 per unit, and Julio’s weekly income is $50.

What is Julio’s marginal rate of substitution of food for clothing when utility is maximized? Explain.

5. Suppose instead that Julio is consuming a bundle with more food and less clothing than his utility maximizing bundle. Would his marginal rate of substitution of food for clothing be greater than or less than your answer in part a? Explain.